对Gonzalo García-Donato、María Eugenia Castellanos、Stefano Cabras、Alicia Quirós和Anabel Forte所著《模型不确定性与缺失数据：一种客观贝叶斯视角》的邀请讨论 (Invited Discussion of "Model Uncertainty and Missing Data: An Objective Bayesian Perspective" by Gonzalo García-Donato , María Eugenia Castellanos , Stefano Cabras Alicia Quirós , and Anabel Forte)

Invited Discussion of "Model Uncertainty and Missing Data: An Objective Bayesian Perspective" by Gonzalo García-Donato , María Eugenia Castellanos , Stefano Cabras Alicia Quirós , and Anabel Forte

翻译：对Gonzalo García-Donato、María Eugenia Castellanos、Stefano Cabras、Alicia Quirós和Anabel Forte所著《模型不确定性与缺失数据：一种客观贝叶斯视角》的邀请讨论

Merlise A Clyde

The article by Garc{í}a-Donato and co-authors addresses the dual challenges of accounting for model uncertainty and missing data within the Gaussian regression frameworks from an objective Bayesian perspective. Thru the use of an imputation $g$-prior that replaces $X_γ^TX_γ$ for model $γ$ in the covariance of $β_γ$ with $Σ_{X_γ}$, the authors develop a coherent approach to addressing the missing data problem and model uncertainty simultaneously with random $X_γ$ in the missing at random (MAR) or missing completely at random (MCAR) settings, while still being computationally tractable. I discuss the connection of the imputation $g$-prior to the $g$-prior with imputed $X$, and to model selection for graphical models that provide an alternative justification for the $g$-prior for random $X$s.

翻译：García-Donato及其合作者的文章从客观贝叶斯视角出发，针对高斯回归框架中同时处理模型不确定性与缺失数据的双重挑战进行了探讨。通过采用一种插补$g$-先验——该先验将模型$γ$中$β_γ$协方差矩阵里的$X_γ^TX_γ$替换为$Σ_{X_γ}$——作者发展了一种在随机缺失（MAR）或完全随机缺失（MCAR）设定下，对随机$X_γ$同时处理缺失数据问题与模型不确定性的连贯方法，且该方法仍保持计算上的可处理性。本文讨论了该插补$g$-先验与基于插补$X$的$g$-先验之间的关联，以及与图模型选择的关系——后者为随机$X$的$g$-先验提供了另一种理论依据。